Additive manufacturing processes are very difficult to model and therefore are hard to predictably control. Example processes such as metal laser sintering (mLS) and electron beam melting (EBM) are incredibly time-consuming to simulate using physics-based finite element modeling. Similarly, other systems that apply a dynamic force to an object or a part being manufactured are extremely time consuming to model.
Additive processes can be characterized by fine-scale finite element meshes. However, meshes that are 10 microns or smaller in size are required to accurately capture the solidification physics around a melt pool for mLS, while the overall part size can be 10,000 times larger than the element size. A uniform mesh size in three dimensions requires more than 108 elements in the first layer and more than 1012 elements in total to fully capture the physics for a single part that fills much of the powder bed. Since mLS and EBM involve the movement of a point heat source to create a part, capturing the physics requires a time step of 10 microseconds or less during laser/electron beam melting, which for a complete build would require more than 1010 total time steps. Such a problem can't be solved as a practical matter. A relatively high-speed supercomputer would take more than 1018 years to solve a problem with this number of elements for this many time steps! The traditional approaches for high-fidelity finite element analysis require over a billion years of computational time to solve a full bed metal laser sintering problem with uniformly small mesh elements. Most models therefore simulate only a small fraction of a part, or simplified “canonical” geometries.
These past efforts have are represented by techniques that model (1) a high-fidelity, multi-physics simulation of a small portion of a larger part; (2) a high-fidelity simulation of a very small part, or (3) a low-fidelity approximation of a small or medium-sized part. Some past efforts use a refinement zone as simulation strategy. The refinement zone may be repeated but is not moved. Past efforts to simulate metal additive manufacturing processes have primarily utilized fine-gridded/static meshing and solution algorithms. See, e.g., Contuzzi, N., Campanelli, S. L. and Ludvico, A. D., “3D Finite Element Analysis in the Selective Laser Melting Process, International Journal of Simulation and Modeling,” Vol. 10, Issue 3, pp. 113-121 (2011); Peyre, P., Aubry, P., Fabbro, R., Neveu, R., and Longuet, A., “Analytical and numerical modelling of the direct metal deposition laser process,” Journal of Physics D: Applied Physics, Vol. 41, Issue 2, pp. 025403 (2008); Shen, N., and Chou, K., “Thermal Modeling of Electron Beam Additive Manufacturing ProcessPowder Sintering Effects,” Proceedings of the ASME 2012 International Manufacturing Science and Engineering Conference MSEC2012-7253 pp. 1-9 (2012); Childs, T. H. C., Hauser, C., and Badrossamay, M., “Selective laser sintering (melting) of stainless and tool steel powders: experiments and modelling. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture,” Vol. 219, Issue 4, pp. 339-357 (2005).
Manufacturing processes generally involve energy insertion in matter by contact or non-contact mechanisms. The introduced energy generally results in changes in the parent materials such as solid-state metal working, addition or removal of material, melting, etc. This introduces structural changes at various length scales. Examples include coarse scale geometric changes visible to the naked eye and microstructural changes responsible for material transitions at finer length scales. In traditional manufacturing processes, contributions to fine length scales are orders of magnitude lower than the coarse length scales of the entire part. Additive manufacturing processes involve energy insertion mechanisms as point or line source(s), which leads to appreciable effects at both micro and macroscopic length scales. Current analysis techniques such as asymptotic and continuum based finite element methods are often too simplistic and tied to coarser length scales and do not incorporate microstructural modes. Similarly, spatial homogenization techniques are tied to finer length scales and extrapolate information on the coarser length scale without computing the coupling between the two length scales. Manufacturing techniques such as forging, welding and wire-drawing have been widely viewed as posing macroscopic boundary conditions. The result is that much manufacturing and control is developed by observation, trial and error rather than simulation.